Many roller coasters today have loops, either as stand-alone loops or as parts of corkscrews. in stand-alone loops, the loops are teardrop shaped and not one complete circle. write a brief essay as to why you think they are constructed that way. be sure to draw on your experience and observations in this virtual lab.

The equation that describes a transverse wave on a string is y = (0.0120 m)sin[(927 rad/s)t - (3.00 rad/m)x] where y is the displacement of a string particle and x is the position of the particle on the string. the wave is traveling in the +x direction. what is the speed v of the wave?

Acoil formed by wrapping 80 turns of wire in the shape of a square is positioned in a magnetic field so that the normal to the plane of the coil makes an angle of 28.0° with the direction of the field. when the magnetic field is increased uniformly from 200 µt to 600 µt in 0.400 as, an emf of magnitude 80.0 mv is induced in the coil. what is the total length of the wire?

Suppose water is leaking from a tank through a circular hole of area ah at its bottom. when water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of water leaving the tank per second to cah 2gh , where c (0 < c < 1) is an empirical constant. a tank in the form of a right-circular cone standing on end, vertex down, is leaking water through a circular hole in its bottom. (assume the removed apex of the cone is of negligible height and volume.) (a) suppose the tank is 20 feet high and has radius 8 feet and the circular hole has radius 2 inches. the differential equation governing the height h in feet of water leaking from a tank after t seconds is dh dt = − 5 6h3/2 . if the height of the water is initially 8 feet, how long will it take the tank to empty? (round your answer to two decimal places.)